Comedians Jon Stewart and Stephen Colbert are about to attempt the impossible: satirising the rightwing TV personality Glenn Beck wth a "Rally to restore sanity" in Washington DC – inspired by a single headline on the social news website Reddit.

In an obvious poke at the stage-managed sanctimony of Beck's "Rally to restore America" earlier this month, Stewart and Colbert will hold duelling rallies on the National Mall on 30 October – just three days before the US congressional midterm elections.

During his Daily Show apearance on Thursday, Stewart announced his plans for a "million moderate march", saying: "Think of our event as Woodstock, but with the nudity and drugs replaced by respectful disagreement."

Not to be outdone, Colbert on his show announced a "March to keep fear alive". In his persona as a parody of a rightwing talkshow host and foil to Stewart, Colbert explained:

"America, the greatest country God ever gave Man, was built on three bedrock principles: Freedom. Liberty. And Fear – that someone might take our freedom and liberty."

"They want to replace our fear with reason. But never forget 'reason' is just one letter away from 'treason,'" said Colbert.

In case anyone thought this was all one big joke, in one respect at least the plan is deadly serious. The National Park Service confirmed that it had received an application from Comedy Central – the cable network behind the Daily Show and Colbert Report – for a permit for a "special event" near the Washington Monument on 30 October.

The impetus for the rally was born online, through the social news aggregator Reddit, a hugely influential US site where users, known as Redditors, submit, vote and comment on links to news items, photos and almost anything of interest online.

But in the wake of Beck's successful rally on 28 August, featuring the likes of Sarah Palin, a Redditor entered a post on the site simply headlined: "I've had a vision and I can't shake it: Stephen Colbert needs to hold a satirical rally in DC."

Mike Schiraldi, a Reddit administrator, explains how the campaign then took off:

One of the neat things about Reddit is that it can serve as a sort of "idea laboratory" – anyone can post something there, and if it strikes a chord with enough people, it'll rocket to the top of the site.

Most submissions don't, but on 31 August, a redditor named MrSamMercer [real name: Joe Laughlin] suggested the idea of a Stephen Colbert rally and it immediately set off a flurry of interest.

It's hard to pinpoint when precisely things started to get real. Everyone had started spontaneously brainstorming, someone registered ColbertRally.com, and others were creating graphics. Back at Reddit HQ, we thought it was a neat project, but we wanted to stay hands-off and let the activity continue unmolested; we try to be as hands-off as possible. Meanwhile, The Colbert Report was on hiatus all week, so everything was operating in a vacuum, but still snowballing.

Then Colbert mentioned the idea and the website on his 7 September episode of the Colbert Report, which set off a fresh wave of enthusiasm, says Schiraldi:

Between the mention on the show, and the mention on our blog, it just sort of took off like a rocket that night; I would say this was the point where I became more or less certain that there was going to be some kind of rally. Perhaps not on the National Mall, perhaps not with the man himself, but something.

Then Joe [aka MrSamMercer] had his second stroke of genius: in order to show that this was more than your average internet petition, we would harness the movement and turn it into a charity drive. He found DonorsChoose, which turned out to be not just an organisation with Stephen Colbert on its board but also one that operated under an innovative social model.

Everyone on Reddit totally ate it up – it was a match made in heaven. I think this would be a cool model for future protests: giving money to good causes until you get your way. Like a hunger strike, except it actually accomplishes something.

Stewart's rally will have firm rules banning portraits adorned with Adolf Hitler-style moustaches, unless on an actual photograph of Hitler or Charlie Chaplin.

"You may be asking yourself, but am I the right person to go to this rally?" Stewart said on his show. "The fact that you would even stop to ask yourself that question, as opposed to just jumping up, grabbing the nearest stack of burnable holy books, strapping on a diaper and pointing your car towards DC – that means I think you just might be right for it."

Colbert, meanwhile, advised "freedom-loving patriots" to bring five extra pairs of underwear to challenge Stewart's "dark, optimistic forces", saying the nation can't afford a rally to restore sanity in the midst of a recession.

Assuming the rallies go ahead – the permit has yet to be finally approved – the real question is whether it is possible to satirise Glenn Beck, a man who once spent half an hour on television explaining the hidden "communist" conspiracy behind the design of Rockefeller Plaza in New York.